How do I replicate this asymmetrical bevel?
but bevel ( the destructive operator ) can do some cool stuff too.


make a cylinder, use the Knife tool (K) to cut a line at the right angle through the cylinder. 


Press Z to set the mode to "cut straight through". 
to make a straight cut: left click the start location, double left click at the final location to end the cut line. Hit Enter to finalize the cut.

inset a circle in the top, and drag it towards the side where you want the shortest radius. Then select the outer edges.





then Ctrl+B (bevel) and press M until the mode is percent. Then add segments using the mouse wheel.


look at the tool information bar at the bottom of the active 3dview.







If you can make it so all fillet edge pairs are similar in length, you'll get nice approximately "circular" fillets.